Optimal. Leaf size=22 \[ x^2+x \left (-5 e^{-3-x}+x+(12+x)^4\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 32, normalized size of antiderivative = 1.45, number of steps used = 5, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {6742, 2194, 2176} \begin {gather*} x^5+48 x^4+864 x^3+6914 x^2-5 e^{-x-3} x+20736 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (20736-5 e^{-3-x}+13828 x+5 e^{-3-x} x+2592 x^2+192 x^3+5 x^4\right ) \, dx\\ &=20736 x+6914 x^2+864 x^3+48 x^4+x^5-5 \int e^{-3-x} \, dx+5 \int e^{-3-x} x \, dx\\ &=5 e^{-3-x}+20736 x-5 e^{-3-x} x+6914 x^2+864 x^3+48 x^4+x^5+5 \int e^{-3-x} \, dx\\ &=20736 x-5 e^{-3-x} x+6914 x^2+864 x^3+48 x^4+x^5\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 29, normalized size = 1.32 \begin {gather*} x \left (20736-5 e^{-3-x}+6914 x+864 x^2+48 x^3+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 38, normalized size = 1.73 \begin {gather*} {\left ({\left (x^{5} + 48 \, x^{4} + 864 \, x^{3} + 6914 \, x^{2} + 20736 \, x\right )} e^{\left (x + 3\right )} - 5 \, x\right )} e^{\left (-x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 43, normalized size = 1.95 \begin {gather*} {\left (x^{5} e^{3} + 48 \, x^{4} e^{3} + 864 \, x^{3} e^{3} + 6914 \, x^{2} e^{3} + 20736 \, x e^{3} - 5 \, x e^{\left (-x\right )}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 32, normalized size = 1.45
method | result | size |
risch | \(x^{5}+48 x^{4}+864 x^{3}+6914 x^{2}+20736 x -5 x \,{\mathrm e}^{-3-x}\) | \(32\) |
derivativedivides | \(\left (3+x \right )^{5}+33 \left (3+x \right )^{4}+378 \left (3+x \right )^{3}+1460 \left (3+x \right )^{2}-6597-2199 x +15 \,{\mathrm e}^{-3-x}-5 \,{\mathrm e}^{-3-x} \left (3+x \right )\) | \(51\) |
default | \(\left (3+x \right )^{5}+33 \left (3+x \right )^{4}+378 \left (3+x \right )^{3}+1460 \left (3+x \right )^{2}-6597-2199 x +15 \,{\mathrm e}^{-3-x}-5 \,{\mathrm e}^{-3-x} \left (3+x \right )\) | \(51\) |
norman | \(\left (x^{5} {\mathrm e}^{3+x}-5 x +6914 x^{2} {\mathrm e}^{3+x}+864 x^{3} {\mathrm e}^{3+x}+48 x^{4} {\mathrm e}^{3+x}+20736 \,{\mathrm e}^{3+x} x \right ) {\mathrm e}^{-3-x}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 41, normalized size = 1.86 \begin {gather*} x^{5} + 48 \, x^{4} + 864 \, x^{3} + 6914 \, x^{2} - 5 \, {\left (x + 1\right )} e^{\left (-x - 3\right )} + 20736 \, x + 5 \, e^{\left (-x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.19, size = 28, normalized size = 1.27 \begin {gather*} x\,\left (6914\,x-5\,{\mathrm {e}}^{-x-3}+864\,x^2+48\,x^3+x^4+20736\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 31, normalized size = 1.41 \begin {gather*} x^{5} + 48 x^{4} + 864 x^{3} + 6914 x^{2} - 5 x e^{- x - 3} + 20736 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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